Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: *rf_harvest_est_nm_wt_thru2023_3e+06__2025-06-08* (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9971

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table X. Unconverged parameters.

## [1]  3  1  0  2 NA

##          variable index     Rhat index_n
## 1 tau_beta2_slope  <NA> 1.203364      NA

area	variable	year	user	species	Rhat
BSAI	Ro_ayu	7			1.289515
BSAI	Ro_ay	7			1.289422
BSAI	Ro_ayu	8			1.278959
BSAI	Ro_ay	8			1.278292
BSAI	Ry_ay	7			1.247618
BSAI	Ry_ayu	7			1.247553
BSAI	Ro_ayu	44			1.240458
BSAI	Ro_ay	44			1.239136
BSAI	Ro_ayu	29			1.238620
BSAI	Ro_ay	29			1.238150
BSAI	Ro_ayu	3			1.227576
BSAI	Ro_ay	3			1.223786
BSAI	Ro_ayu	12			1.215138
BSAI	Ry_ayg	15			1.212564
BSAI	Ro_ay	12			1.211061
BSAI	Ro_ayu	43			1.204786
BSAI	Ro_ay	43			1.202564
BSAI	Rb_ayu	10			1.201175
BSAI	Ro_ayu	11			1.199253
BSAI	Rp_ayu	10			1.198552
BSAI	R_ayu	10			1.198352
BSAI	Ro_ay	11			1.196522
BSAI	Rb_ay	10			1.196021
BSAI	Rp_ay	10			1.193324
BSAI	R_ay	10			1.193031
BSAI	Ro_ayu	13			1.189761
BSAI	Ry_ayu	18			1.187908
BSAI	Ry_ayg	8			1.183686
BSAI	Ro_ayg	4			1.182951
BSAI	Ry_ayg	18			1.181138
BSAI	Ry_ay	18			1.176250
BSAI	H_ayu	10			1.171104
BSAI	Ro_ayu	40			1.170907
BSAI	Ry_ayg	11			1.170101
BSAI	Hb_ayu	10			1.169720
BSAI	Ro_ay	4			1.169142
BSAI	Ro_ayg	13			1.168547
BSAI	Ry_ay	20			1.168005
BSAI	Hp_ayu	10			1.167915
BSAI	Ry_ayu	20			1.165533
BSAI	Ro_ay	40			1.163968
BSAI	Ro_ayu	9			1.163792
BSAI	Ro_ay	9			1.156401
BSAI	Ry_ayu	28			1.153717
BSAI	Hb_ay	10			1.153437
BSAI	Hy_ayg	3			1.153026
BSAI	Ro_ayu	4			1.152817
BSAI	Hp_ay	10			1.151909
BSAI	H_ay	10			1.151476
BSAI	Ro_ayg	16			1.150310
BSAI	Ry_ay	28			1.149596
BSAI	Ro_ay	13			1.149258
BSAI	Ro_ayu	10			1.142740
BSAI	Ry_ay	4			1.142707
BSAI	Ro_ayu	41			1.140923
BSAI	Ro_ayu	2			1.139452
BSAI	Ro_ay	41			1.138435
BSAI	Ro_ayg	1			1.136301
BSAI	Ro_ay	2			1.133424
BSAI	Ry_ayg	9			1.133415
BSAI	Hy_ayu	10			1.133148
BSAI	Ro_ay	10			1.130224
BSAI	Ry_ayg	21			1.129706
BSAI	Ro_ayu	36			1.127807
BSAI	Ro_ay	36			1.126235
BSAI	Ro_ayu	17			1.126198
BSAI	Ry_ayu	4			1.123696
BSAI	Ro_ayu	37			1.123308
BSAI	Hy_ay	10			1.122866
BSAI	Ro_ayu	25			1.122420
BSAI	Rp_ayg	14			1.121566
BSAI	Ro_ayu	14			1.120851
BSAI	Ro_ay	37			1.120217
BSAI	Ro_ay	25			1.119317
BSAI	R_ayg	14			1.118741
BSAI	Ro_ay	17			1.116339
BSAI	Ry_ayu	9			1.115860
BSAI	Ro_ayg	20			1.114785
BSAI	Ro_ayg	7			1.114566
BSAI	Ho_ayu	11			1.111867
CI	Ro_ayu	6			1.154241
CI	tau_beta1_black				1.147891
CI	Ro_ay	6			1.128774
CI	R_ayu	6			1.116724
CSEO	pH	47	2	2	1.151249
CSEO	pH	46	2	2	1.121781
CSEO	pH	45	2	2	1.116405
EWYKT	beta1_dsr				1.170934
EWYKT	p_dsr	29	1		1.169228
EWYKT	p_dsr	15	2		1.153081
EWYKT	p_dsr	3	2		1.143496
EWYKT	p_dsr	29	2		1.140725
EWYKT	p_dsr	6	1		1.134414
EWYKT	Rs_ayu	18			1.132715
NG	Ro_ayu	12			1.148070
NG	mu_beta2_pH			1	1.135154
NG	Ro_ay	12			1.132014
NSEI	beta2_pelagic				1.164295
NSEO	Ry_ayg	8			1.130843
NSEO	Rs_ayu	20			1.115677
NSEO	Rdnye_ayu	44			1.112313
PWSI	beta1_pelagic				1.138339
PWSI	beta1_pH			2	1.127972
PWSI	beta2_pelagic				1.124632
PWSI	beta0_pelagic				1.118883
PWSO	beta1_pH			2	1.255959
PWSO	beta0_pelagic				1.154732
PWSO	Ro_ayg	10			1.124090
SOKO2SAP	Ro_ayu	8			1.240603
SOKO2SAP	Ro_ay	8			1.235025
SOKO2SAP	Ro_ayu	6			1.222857
SOKO2SAP	Ro_ayu	4			1.217302
SOKO2SAP	Ro_ay	6			1.209331
SOKO2SAP	Ro_ay	4			1.200623
SOKO2SAP	Rp_ayu	1			1.190479
SOKO2SAP	R_ayu	1			1.190217
SOKO2SAP	Rb_ayu	1			1.187755
SOKO2SAP	Rp_ay	1			1.187621
SOKO2SAP	R_ay	1			1.187278
SOKO2SAP	Rb_ay	1			1.185125
SOKO2SAP	beta1_pH			3	1.183784
SOKO2SAP	Ro_ayu	7			1.159351
SOKO2SAP	beta4_pelagic				1.144051
SOKO2SAP	Ry_ayu	17			1.141310
SOKO2SAP	Ro_ay	7			1.140390
SOKO2SAP	Ry_ay	17			1.137240
SOKO2SAP	Ro_ayu	2			1.132917
SOKO2SAP	Ro_ayu	30			1.132727
SOKO2SAP	Ro_ay	30			1.131246
SOKO2SAP	Ro_ay	2			1.130836
SOKO2SAP	Rb_ayu	6			1.128360
SOKO2SAP	Rb_ay	6			1.125331
SOKO2SAP	Rp_ayu	6			1.125100
SOKO2SAP	Ro_ayg	3			1.124743
SOKO2SAP	R_ayu	6			1.124736
SOKO2SAP	Rp_ay	6			1.122022
SOKO2SAP	R_ay	6			1.121545
SOKO2SAP	Rp_ayu	4			1.121435
SOKO2SAP	R_ayu	4			1.121043
SOKO2SAP	Rb_ay	3			1.120989
SOKO2SAP	Rb_ayu	3			1.120135
SOKO2SAP	Rp_ay	4			1.120013
SOKO2SAP	R_ay	4			1.119568
SOKO2SAP	Ry_ayu	18			1.118856
SOKO2SAP	Rp_ayu	3			1.118499
SOKO2SAP	R_ayu	3			1.118356
SOKO2SAP	Rp_ay	3			1.118148
SOKO2SAP	R_ay	3			1.117876
SOKO2SAP	Ry_ay	18			1.117494
SOKO2SAP	Rb_ayu	4			1.115677
SOKO2SAP	Rb_ay	4			1.114430
SOKO2SAP	Ro_ayu	16			1.114077
SSEI	lambda_H				1.274730
SSEI	pH	45	2	2	1.154535
SSEI	pH	47	2	2	1.128255
SSEO	Rp_ayu	3			1.128743
SSEO	Rb_ayu	1			1.127580
SSEO	Rb_ayu	3			1.126252
SSEO	Rp_ayu	2			1.126014
SSEO	Rb_ayu	2			1.124639
SSEO	R_ayu	3			1.121612
SSEO	Rp_ayu	1			1.117196
WKMA	beta2_pH			1	1.274047
WKMA	Ro_ayu	9			1.141892
WKMA	Ro_ay	9			1.126323
WKMA	beta1_pH			1	1.116633
WKMA	beta0_pH			1	1.114032
afognak	Ro_ayu	16			1.198001
afognak	Ro_ay	16			1.173554
afognak	Ry_ayu	12			1.169819
afognak	Ry_ay	12			1.167018
afognak	Hy_ayu	12			1.146442
afognak	Ho_ayu	18			1.125921
eastside	Ry_ayg	25			1.194423
eastside	Hy_ayu	20			1.159150
eastside	Ry_ayu	8			1.158094
eastside	Ry_ay	8			1.153888
eastside	Ro_ayu	12			1.149363
eastside	Ro_ayu	7			1.135179
eastside	Hy_ayu	35			1.125312
eastside	Ro_ayu	2			1.123124
eastside	Ro_ayu	24			1.116545
eastside	Ro_ayg	8			1.113801
eastside	Ro_ayu	21			1.110660
northeast	Ry_ayu	9			1.120526
northeast	Ry_ay	9			1.119536
	tau_beta2_slope				1.203364

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.125	0.075	-0.261	-0.128	0.036
mu_bc_H[2]	-0.096	0.044	-0.171	-0.099	-0.001
mu_bc_H[3]	-0.434	0.070	-0.565	-0.437	-0.289
mu_bc_H[4]	-0.991	0.193	-1.377	-0.990	-0.617
mu_bc_H[5]	0.902	0.920	-0.184	0.721	3.214
mu_bc_H[6]	-2.158	0.313	-2.752	-2.155	-1.556
mu_bc_H[7]	-0.458	0.109	-0.683	-0.453	-0.250
mu_bc_H[8]	0.248	0.354	-0.325	0.220	1.050
mu_bc_H[9]	-0.291	0.133	-0.541	-0.294	-0.021
mu_bc_H[10]	-0.099	0.071	-0.227	-0.102	0.047
mu_bc_H[11]	-0.123	0.038	-0.196	-0.123	-0.049
mu_bc_H[12]	-0.254	0.109	-0.492	-0.250	-0.051
mu_bc_H[13]	-0.137	0.077	-0.288	-0.139	0.018
mu_bc_H[14]	-0.306	0.096	-0.503	-0.301	-0.133
mu_bc_H[15]	-0.342	0.049	-0.437	-0.342	-0.243
mu_bc_H[16]	-0.262	0.371	-0.913	-0.291	0.566
mu_bc_R[1]	1.317	0.142	1.045	1.316	1.601
mu_bc_R[2]	1.454	0.095	1.269	1.454	1.643
mu_bc_R[3]	1.392	0.144	1.105	1.392	1.679
mu_bc_R[4]	0.916	0.197	0.506	0.923	1.276
mu_bc_R[5]	1.198	0.456	0.286	1.207	2.062
mu_bc_R[6]	-1.587	0.407	-2.394	-1.579	-0.813
mu_bc_R[7]	0.444	0.212	0.009	0.450	0.845
mu_bc_R[8]	0.536	0.188	0.152	0.540	0.890
mu_bc_R[9]	0.326	0.203	-0.106	0.342	0.688
mu_bc_R[10]	1.309	0.167	0.969	1.315	1.615
mu_bc_R[11]	1.037	0.097	0.853	1.036	1.223
mu_bc_R[12]	0.820	0.203	0.417	0.823	1.205
mu_bc_R[13]	1.029	0.102	0.829	1.029	1.223
mu_bc_R[14]	0.895	0.143	0.602	0.894	1.168
mu_bc_R[15]	0.782	0.110	0.566	0.785	0.993
mu_bc_R[16]	1.093	0.127	0.833	1.095	1.333
tau_pH[1]	5.122	0.436	4.311	5.107	6.037
tau_pH[2]	1.971	0.223	1.566	1.961	2.433
tau_pH[3]	2.150	0.220	1.739	2.145	2.599
beta0_pH[1,1]	0.558	0.173	0.206	0.564	0.874
beta0_pH[2,1]	1.367	0.184	0.995	1.372	1.704
beta0_pH[3,1]	1.428	0.193	1.024	1.440	1.772
beta0_pH[4,1]	1.565	0.217	1.090	1.580	1.940
beta0_pH[5,1]	-0.863	0.301	-1.530	-0.840	-0.354
beta0_pH[6,1]	-0.758	0.560	-2.030	-0.655	-0.079
beta0_pH[7,1]	-0.489	0.576	-1.980	-0.439	0.500
beta0_pH[8,1]	-0.664	0.271	-1.265	-0.636	-0.203
beta0_pH[9,1]	-0.643	0.283	-1.270	-0.621	-0.134
beta0_pH[10,1]	0.348	0.218	-0.128	0.365	0.729
beta0_pH[11,1]	-0.068	0.168	-0.408	-0.061	0.253
beta0_pH[12,1]	0.483	0.187	0.119	0.488	0.845
beta0_pH[13,1]	0.006	0.143	-0.268	0.006	0.289
beta0_pH[14,1]	-0.303	0.167	-0.645	-0.295	0.007
beta0_pH[15,1]	-0.019	0.178	-0.375	-0.016	0.331
beta0_pH[16,1]	-0.472	0.403	-1.405	-0.395	0.063
beta0_pH[1,2]	2.828	0.161	2.498	2.833	3.115
beta0_pH[2,2]	2.886	0.140	2.606	2.886	3.159
beta0_pH[3,2]	3.129	0.160	2.837	3.125	3.438
beta0_pH[4,2]	2.949	0.132	2.690	2.952	3.203
beta0_pH[5,2]	4.757	1.391	2.936	4.483	8.535
beta0_pH[6,2]	3.119	0.209	2.715	3.121	3.526
beta0_pH[7,2]	1.831	0.200	1.433	1.829	2.222
beta0_pH[8,2]	2.871	0.175	2.537	2.866	3.228
beta0_pH[9,2]	3.438	0.220	3.019	3.432	3.875
beta0_pH[10,2]	3.686	0.212	3.260	3.682	4.108
beta0_pH[11,2]	-4.848	0.296	-5.422	-4.852	-4.248
beta0_pH[12,2]	-4.786	0.404	-5.596	-4.780	-4.005
beta0_pH[13,2]	-4.563	0.405	-5.348	-4.582	-3.746
beta0_pH[14,2]	-5.595	0.492	-6.624	-5.568	-4.729
beta0_pH[15,2]	-4.289	0.343	-4.930	-4.291	-3.607
beta0_pH[16,2]	-4.860	0.377	-5.622	-4.848	-4.118
beta0_pH[1,3]	-0.108	0.702	-1.674	-0.026	1.009
beta0_pH[2,3]	2.195	0.159	1.885	2.194	2.514
beta0_pH[3,3]	2.528	0.147	2.243	2.528	2.820
beta0_pH[4,3]	2.967	0.161	2.650	2.967	3.279
beta0_pH[5,3]	2.151	1.314	0.502	1.883	5.463
beta0_pH[6,3]	0.995	0.493	-0.188	1.031	1.843
beta0_pH[7,3]	0.633	0.175	0.300	0.629	0.985
beta0_pH[8,3]	0.304	0.187	-0.063	0.309	0.661
beta0_pH[9,3]	-0.644	0.393	-1.667	-0.606	0.001
beta0_pH[10,3]	0.475	0.378	-0.458	0.521	1.080
beta0_pH[11,3]	-0.164	0.329	-0.809	-0.174	0.480
beta0_pH[12,3]	-0.853	0.358	-1.640	-0.826	-0.236
beta0_pH[13,3]	-0.112	0.311	-0.715	-0.116	0.492
beta0_pH[14,3]	-0.280	0.263	-0.806	-0.277	0.235
beta0_pH[15,3]	-0.714	0.310	-1.350	-0.695	-0.176
beta0_pH[16,3]	-0.381	0.289	-0.957	-0.383	0.204
beta1_pH[1,1]	3.068	0.323	2.490	3.047	3.784
beta1_pH[2,1]	2.157	0.307	1.647	2.132	2.787
beta1_pH[3,1]	1.971	0.310	1.441	1.944	2.619
beta1_pH[4,1]	2.398	0.362	1.833	2.351	3.201
beta1_pH[5,1]	2.296	0.367	1.701	2.260	3.099
beta1_pH[6,1]	3.862	1.163	2.319	3.623	6.793
beta1_pH[7,1]	2.592	1.120	0.775	2.480	5.519
beta1_pH[8,1]	4.052	1.036	2.629	3.824	6.680
beta1_pH[9,1]	2.319	0.373	1.668	2.285	3.183
beta1_pH[10,1]	2.225	0.311	1.713	2.198	2.886
beta1_pH[11,1]	3.242	0.212	2.843	3.237	3.659
beta1_pH[12,1]	2.551	0.220	2.123	2.551	2.985
beta1_pH[13,1]	2.962	0.213	2.540	2.964	3.390
beta1_pH[14,1]	3.404	0.218	2.989	3.401	3.848
beta1_pH[15,1]	2.519	0.224	2.086	2.515	2.983
beta1_pH[16,1]	4.121	0.772	3.163	3.973	5.911
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.006	0.080	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.003	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.687	0.332	6.021	6.687	7.322
beta1_pH[12,2]	6.446	0.464	5.588	6.423	7.392
beta1_pH[13,2]	6.939	0.442	6.069	6.947	7.826
beta1_pH[14,2]	7.239	0.518	6.317	7.212	8.341
beta1_pH[15,2]	6.757	0.377	6.010	6.753	7.495
beta1_pH[16,2]	7.454	0.414	6.643	7.447	8.288
beta1_pH[1,3]	4.647	1.623	2.118	4.409	8.159
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.886	6.283	0.786	2.808	12.687
beta1_pH[6,3]	3.484	4.842	0.368	2.654	13.790
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.750	0.346	2.076	2.741	3.455
beta1_pH[9,3]	2.756	0.457	2.018	2.713	3.860
beta1_pH[10,3]	2.897	0.458	2.141	2.844	3.959
beta1_pH[11,3]	2.746	0.389	2.014	2.742	3.519
beta1_pH[12,3]	4.095	0.448	3.252	4.076	4.974
beta1_pH[13,3]	1.696	0.334	1.033	1.695	2.335
beta1_pH[14,3]	2.528	0.336	1.891	2.519	3.188
beta1_pH[15,3]	2.004	0.335	1.411	1.988	2.690
beta1_pH[16,3]	1.795	0.321	1.155	1.798	2.433
beta2_pH[1,1]	0.482	0.127	0.294	0.464	0.775
beta2_pH[2,1]	0.580	0.300	0.253	0.519	1.263
beta2_pH[3,1]	0.659	0.480	0.223	0.558	1.825
beta2_pH[4,1]	0.479	0.205	0.213	0.442	0.952
beta2_pH[5,1]	1.483	1.015	0.244	1.338	3.922
beta2_pH[6,1]	0.180	0.064	0.082	0.171	0.326
beta2_pH[7,1]	0.032	0.265	0.000	0.000	0.185
beta2_pH[8,1]	0.241	0.102	0.123	0.226	0.440
beta2_pH[9,1]	0.441	0.249	0.181	0.394	0.962
beta2_pH[10,1]	0.611	0.264	0.272	0.560	1.251
beta2_pH[11,1]	0.795	0.210	0.476	0.757	1.311
beta2_pH[12,1]	1.358	0.513	0.730	1.242	2.583
beta2_pH[13,1]	0.751	0.234	0.415	0.717	1.311
beta2_pH[14,1]	0.837	0.219	0.521	0.801	1.372
beta2_pH[15,1]	0.827	0.314	0.418	0.762	1.620
beta2_pH[16,1]	0.386	0.181	0.157	0.340	0.851
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-1.999	1.819	-6.747	-1.511	-0.032
beta2_pH[4,2]	-2.032	1.907	-6.896	-1.509	-0.025
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.554	4.370	-20.644	-8.546	-4.036
beta2_pH[12,2]	-8.145	5.044	-20.388	-7.251	-1.020
beta2_pH[13,2]	-7.941	4.997	-20.233	-6.909	-1.665
beta2_pH[14,2]	-8.638	4.742	-20.589	-7.582	-2.539
beta2_pH[15,2]	-9.382	4.418	-20.390	-8.323	-3.796
beta2_pH[16,2]	-9.481	4.348	-20.488	-8.467	-3.910
beta2_pH[1,3]	0.241	0.270	0.101	0.182	0.690
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	9.074	6.266	-0.073	8.256	23.518
beta2_pH[6,3]	9.080	6.347	0.182	8.028	23.900
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	10.032	5.797	1.776	8.864	24.171
beta2_pH[9,3]	9.040	6.398	0.499	7.868	23.833
beta2_pH[10,3]	8.508	6.529	0.507	7.469	23.657
beta2_pH[11,3]	-2.374	2.151	-9.029	-1.730	-0.645
beta2_pH[12,3]	-2.528	2.150	-9.099	-1.886	-0.926
beta2_pH[13,3]	-2.949	2.386	-10.161	-2.162	-0.790
beta2_pH[14,3]	-2.884	2.289	-9.277	-2.158	-0.928
beta2_pH[15,3]	-3.063	2.426	-9.905	-2.254	-1.009
beta2_pH[16,3]	-3.117	2.506	-10.314	-2.269	-0.961
beta3_pH[1,1]	35.957	0.825	34.387	35.966	37.633
beta3_pH[2,1]	33.532	1.203	31.442	33.409	36.076
beta3_pH[3,1]	33.657	1.050	31.619	33.640	35.848
beta3_pH[4,1]	33.862	1.252	31.626	33.770	36.623
beta3_pH[5,1]	27.675	1.093	26.407	27.451	30.979
beta3_pH[6,1]	38.168	3.210	32.272	37.982	44.784
beta3_pH[7,1]	30.642	8.035	18.600	30.058	45.168
beta3_pH[8,1]	40.062	2.191	36.295	39.776	45.060
beta3_pH[9,1]	30.663	1.477	28.106	30.562	33.965
beta3_pH[10,1]	32.963	0.984	31.107	32.947	34.950
beta3_pH[11,1]	30.340	0.473	29.451	30.332	31.307
beta3_pH[12,1]	30.153	0.402	29.354	30.152	30.941
beta3_pH[13,1]	33.152	0.582	32.010	33.132	34.352
beta3_pH[14,1]	32.039	0.463	31.163	32.022	32.978
beta3_pH[15,1]	31.207	0.649	29.902	31.215	32.477
beta3_pH[16,1]	32.092	1.100	30.407	31.925	34.744
beta3_pH[1,2]	30.029	8.001	18.477	29.109	45.058
beta3_pH[2,2]	30.026	7.930	18.610	29.079	44.765
beta3_pH[3,2]	30.134	8.044	18.554	28.940	44.961
beta3_pH[4,2]	30.058	7.939	18.544	29.298	44.827
beta3_pH[5,2]	29.759	7.839	18.441	28.692	44.638
beta3_pH[6,2]	30.062	7.949	18.489	29.094	45.013
beta3_pH[7,2]	29.898	7.852	18.520	28.899	44.917
beta3_pH[8,2]	29.796	7.959	18.381	28.723	45.033
beta3_pH[9,2]	30.154	7.921	18.559	29.403	44.939
beta3_pH[10,2]	29.978	7.887	18.481	28.913	44.944
beta3_pH[11,2]	43.399	0.180	43.110	43.383	43.769
beta3_pH[12,2]	43.193	0.194	42.943	43.147	43.727
beta3_pH[13,2]	43.864	0.152	43.469	43.907	44.044
beta3_pH[14,2]	43.305	0.205	43.047	43.251	43.801
beta3_pH[15,2]	43.408	0.197	43.100	43.388	43.812
beta3_pH[16,2]	43.496	0.186	43.165	43.495	43.836
beta3_pH[1,3]	39.227	3.239	33.070	39.095	45.371
beta3_pH[2,3]	30.363	8.020	18.413	29.772	44.946
beta3_pH[3,3]	30.010	7.840	18.458	29.263	44.736
beta3_pH[4,3]	30.226	7.982	18.466	29.540	44.960
beta3_pH[5,3]	36.668	3.862	31.208	36.088	45.040
beta3_pH[6,3]	40.442	3.431	31.858	40.756	45.620
beta3_pH[7,3]	37.964	4.228	31.368	37.834	45.363
beta3_pH[8,3]	41.491	0.254	41.055	41.491	41.934
beta3_pH[9,3]	33.451	0.583	31.572	33.527	34.231
beta3_pH[10,3]	35.850	0.780	33.564	36.026	36.860
beta3_pH[11,3]	41.810	0.812	40.135	41.843	43.274
beta3_pH[12,3]	41.728	0.397	40.962	41.737	42.492
beta3_pH[13,3]	42.714	0.900	41.030	42.704	44.720
beta3_pH[14,3]	41.107	0.575	39.915	41.135	42.162
beta3_pH[15,3]	42.649	0.651	41.252	42.711	43.753
beta3_pH[16,3]	42.904	0.737	41.116	43.015	44.056
beta4_pH[1,1]	0.901	0.695	-0.095	0.810	2.415
beta4_pH[2,1]	1.179	0.983	-0.046	0.942	3.873
beta4_pH[3,1]	0.299	0.935	-1.117	0.215	2.429
beta4_pH[4,1]	0.609	1.254	-1.319	0.505	3.582
beta4_pH[5,1]	-0.615	0.619	-1.957	-0.553	0.405
beta4_pH[6,1]	-0.623	0.591	-1.870	-0.591	0.363
beta4_pH[7,1]	0.343	1.311	-1.555	0.082	3.805
beta4_pH[8,1]	-0.075	1.034	-1.507	-0.236	2.591
beta4_pH[9,1]	0.449	1.298	-1.313	0.114	3.812
beta4_pH[10,1]	0.646	1.241	-0.651	0.245	4.152
beta4_pH[11,1]	0.682	1.429	-1.376	0.463	4.178
beta4_pH[12,1]	0.964	1.554	-1.290	0.712	4.805
beta4_pH[13,1]	1.782	1.516	-0.257	1.479	5.639
beta4_pH[14,1]	2.016	1.626	-0.102	1.665	6.186
beta4_pH[15,1]	0.374	1.292	-1.335	0.162	3.655
beta4_pH[16,1]	0.637	1.391	-1.310	0.400	4.267
beta4_pH[1,2]	-3.240	0.862	-3.967	-3.432	-0.903
beta4_pH[2,2]	0.423	2.025	-1.987	-0.157	5.630
beta4_pH[3,2]	-0.861	2.158	-3.241	-1.547	4.971
beta4_pH[4,2]	1.638	1.968	-0.942	1.202	6.419
beta4_pH[5,2]	0.058	2.395	-3.537	-0.269	5.660
beta4_pH[6,2]	-0.337	2.430	-3.790	-0.694	5.142
beta4_pH[7,2]	0.060	0.931	-1.703	0.025	1.941
beta4_pH[8,2]	-0.763	2.149	-3.398	-1.348	4.626
beta4_pH[9,2]	-0.392	2.341	-3.728	-0.711	5.008
beta4_pH[10,2]	-2.436	2.093	-3.987	-3.491	3.176
beta4_pH[11,2]	-0.446	0.632	-1.312	-0.544	1.032
beta4_pH[12,2]	-1.072	1.035	-2.509	-1.222	1.614
beta4_pH[13,2]	-1.562	0.863	-2.858	-1.664	0.367
beta4_pH[14,2]	-0.131	1.049	-1.441	-0.341	2.665
beta4_pH[15,2]	-1.711	0.776	-2.877	-1.825	-0.020
beta4_pH[16,2]	-0.882	1.027	-2.230	-1.071	1.727
beta4_pH[1,3]	-0.346	1.583	-2.252	-0.759	4.105
beta4_pH[2,3]	-1.294	0.662	-2.197	-1.389	0.216
beta4_pH[3,3]	-1.636	0.817	-2.714	-1.768	0.292
beta4_pH[4,3]	-0.301	1.426	-1.876	-0.702	3.700
beta4_pH[5,3]	0.330	1.939	-3.411	0.208	5.035
beta4_pH[6,3]	0.461	1.816	-2.649	0.271	4.848
beta4_pH[7,3]	0.341	1.733	-2.350	0.114	4.545
beta4_pH[8,3]	0.719	1.661	-1.635	0.421	4.964
beta4_pH[9,3]	0.918	1.695	-1.524	0.625	5.183
beta4_pH[10,3]	0.165	1.667	-2.250	-0.111	4.456
beta4_pH[11,3]	0.886	1.172	-0.543	0.593	3.892
beta4_pH[12,3]	0.580	1.104	-0.994	0.385	3.342
beta4_pH[13,3]	0.033	0.625	-0.922	-0.046	1.481
beta4_pH[14,3]	0.341	0.941	-0.930	0.168	2.710
beta4_pH[15,3]	0.152	0.570	-0.731	0.081	1.536
beta4_pH[16,3]	0.628	0.976	-0.531	0.406	3.163
beta0_pelagic[1]	2.226	0.133	1.967	2.222	2.491
beta0_pelagic[2]	1.511	0.128	1.258	1.511	1.752
beta0_pelagic[3]	-0.601	0.882	-2.568	-0.394	0.573
beta0_pelagic[4]	-0.494	1.177	-4.483	-0.180	0.813
beta0_pelagic[5]	1.192	0.254	0.660	1.193	1.689
beta0_pelagic[6]	1.466	0.269	0.887	1.484	1.948
beta0_pelagic[7]	1.598	0.210	1.215	1.588	2.046
beta0_pelagic[8]	1.764	0.198	1.372	1.755	2.190
beta0_pelagic[9]	2.471	0.318	1.858	2.472	3.057
beta0_pelagic[10]	2.502	0.210	2.057	2.512	2.897
beta0_pelagic[11]	0.155	0.427	-0.815	0.255	0.736
beta0_pelagic[12]	1.679	0.145	1.396	1.674	1.968
beta0_pelagic[13]	0.280	0.235	-0.289	0.308	0.656
beta0_pelagic[14]	-0.090	0.270	-0.704	-0.068	0.381
beta0_pelagic[15]	-0.263	0.142	-0.544	-0.264	0.011
beta0_pelagic[16]	0.263	0.303	-0.558	0.332	0.664
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	2.249	1.479	0.524	1.784	5.778
beta1_pelagic[4]	1.887	1.316	0.377	1.510	5.790
beta1_pelagic[5]	-0.076	0.313	-0.681	-0.077	0.540
beta1_pelagic[6]	-0.100	0.454	-0.870	-0.148	0.765
beta1_pelagic[7]	-0.020	0.291	-0.588	-0.018	0.540
beta1_pelagic[8]	-0.007	0.277	-0.561	-0.007	0.528
beta1_pelagic[9]	0.210	0.487	-0.750	0.323	0.970
beta1_pelagic[10]	0.068	0.275	-0.458	0.067	0.638
beta1_pelagic[11]	3.418	1.000	2.091	3.212	5.763
beta1_pelagic[12]	2.775	0.316	2.182	2.770	3.413
beta1_pelagic[13]	2.954	0.719	1.800	2.868	4.582
beta1_pelagic[14]	4.383	1.089	2.817	4.178	6.802
beta1_pelagic[15]	2.914	0.262	2.406	2.913	3.445
beta1_pelagic[16]	3.673	0.990	2.697	3.318	6.623
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.486	1.343	0.030	0.150	3.691
beta2_pelagic[4]	1.283	3.117	0.033	0.373	11.387
beta2_pelagic[5]	-0.010	0.675	-1.401	-0.010	1.438
beta2_pelagic[6]	-0.107	0.671	-1.452	-0.154	1.298
beta2_pelagic[7]	0.013	0.643	-1.352	-0.001	1.392
beta2_pelagic[8]	0.002	0.635	-1.408	-0.002	1.329
beta2_pelagic[9]	0.206	0.684	-1.306	0.254	1.539
beta2_pelagic[10]	0.039	0.623	-1.246	0.027	1.392
beta2_pelagic[11]	2.573	5.231	0.125	0.348	16.575
beta2_pelagic[12]	6.291	5.590	0.980	4.655	21.631
beta2_pelagic[13]	1.001	2.751	0.171	0.448	5.942
beta2_pelagic[14]	0.323	0.156	0.160	0.291	0.720
beta2_pelagic[15]	6.423	5.130	1.250	4.948	20.828
beta2_pelagic[16]	4.701	5.859	0.181	2.818	20.100
beta3_pelagic[1]	29.765	7.959	18.399	28.736	44.929
beta3_pelagic[2]	29.785	7.867	18.484	28.460	44.769
beta3_pelagic[3]	28.932	6.504	18.750	28.248	43.737
beta3_pelagic[4]	24.827	4.870	18.335	24.194	39.118
beta3_pelagic[5]	29.968	8.156	18.421	28.388	45.119
beta3_pelagic[6]	31.826	6.755	18.953	31.703	44.531
beta3_pelagic[7]	29.773	7.899	18.436	28.696	44.955
beta3_pelagic[8]	29.721	8.134	18.408	28.263	44.992
beta3_pelagic[9]	30.627	6.078	19.111	30.601	42.910
beta3_pelagic[10]	29.357	8.207	18.345	27.872	45.031
beta3_pelagic[11]	42.437	1.680	38.248	42.979	45.239
beta3_pelagic[12]	43.477	0.289	43.003	43.467	43.982
beta3_pelagic[13]	42.696	1.340	39.974	42.676	45.389
beta3_pelagic[14]	42.500	1.717	39.134	42.480	45.674
beta3_pelagic[15]	43.167	0.282	42.473	43.176	43.690
beta3_pelagic[16]	43.111	0.814	41.094	43.196	45.018
mu_beta0_pelagic[1]	0.636	1.158	-2.041	0.710	2.862
mu_beta0_pelagic[2]	1.803	0.396	1.008	1.804	2.579
mu_beta0_pelagic[3]	0.341	0.453	-0.602	0.352	1.271
tau_beta0_pelagic[1]	0.445	0.500	0.048	0.278	1.866
tau_beta0_pelagic[2]	2.841	3.236	0.248	2.058	9.726
tau_beta0_pelagic[3]	1.578	1.211	0.167	1.266	4.714
beta0_yellow[1]	-0.532	0.194	-0.987	-0.515	-0.213
beta0_yellow[2]	0.505	0.163	0.159	0.511	0.799
beta0_yellow[3]	-0.315	0.191	-0.713	-0.309	0.022
beta0_yellow[4]	0.832	0.315	-0.053	0.894	1.212
beta0_yellow[5]	-0.282	0.354	-0.952	-0.279	0.414
beta0_yellow[6]	1.111	0.168	0.789	1.112	1.441
beta0_yellow[7]	0.983	0.155	0.687	0.976	1.295
beta0_yellow[8]	1.011	0.153	0.716	1.009	1.310
beta0_yellow[9]	0.661	0.161	0.345	0.656	0.973
beta0_yellow[10]	0.592	0.142	0.308	0.594	0.874
beta0_yellow[11]	-1.979	0.486	-2.929	-1.987	-1.032
beta0_yellow[12]	-3.710	0.420	-4.603	-3.695	-2.946
beta0_yellow[13]	-3.738	0.486	-4.783	-3.717	-2.856
beta0_yellow[14]	-2.162	0.550	-3.162	-2.185	-0.883
beta0_yellow[15]	-2.877	0.447	-3.805	-2.856	-2.047
beta0_yellow[16]	-2.398	0.467	-3.318	-2.404	-1.432
beta1_yellow[1]	0.857	1.483	0.010	0.667	2.717
beta1_yellow[2]	1.065	0.358	0.582	1.026	1.701
beta1_yellow[3]	0.705	0.264	0.247	0.692	1.250
beta1_yellow[4]	1.377	0.813	0.617	1.170	4.013
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.121	0.479	1.182	2.117	3.066
beta1_yellow[12]	2.507	0.437	1.690	2.486	3.423
beta1_yellow[13]	2.861	0.491	2.005	2.835	3.908
beta1_yellow[14]	2.234	0.532	1.098	2.254	3.248
beta1_yellow[15]	2.125	0.440	1.302	2.100	3.044
beta1_yellow[16]	2.156	0.476	1.221	2.163	3.083
beta2_yellow[1]	-4.084	3.318	-12.102	-3.334	-0.091
beta2_yellow[2]	-4.190	3.489	-12.545	-3.180	-0.230
beta2_yellow[3]	-3.935	3.466	-13.554	-3.010	-0.160
beta2_yellow[4]	-3.353	3.277	-11.326	-2.312	-0.085
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.501	2.651	-11.461	-3.919	-1.099
beta2_yellow[12]	-4.852	2.537	-11.377	-4.321	-1.444
beta2_yellow[13]	-4.625	2.484	-10.760	-4.041	-1.497
beta2_yellow[14]	-4.650	2.738	-11.539	-4.123	-0.674
beta2_yellow[15]	-4.346	2.668	-11.211	-3.713	-1.040
beta2_yellow[16]	-4.875	2.646	-11.347	-4.314	-1.372
beta3_yellow[1]	25.820	7.207	18.245	22.608	44.127
beta3_yellow[2]	29.100	1.759	26.290	28.860	32.811
beta3_yellow[3]	32.955	3.058	26.339	32.844	39.556
beta3_yellow[4]	29.009	3.487	21.503	28.000	35.921
beta3_yellow[5]	29.993	7.918	18.448	29.055	44.822
beta3_yellow[6]	30.139	8.033	18.492	29.256	44.982
beta3_yellow[7]	30.089	7.921	18.526	29.169	45.049
beta3_yellow[8]	29.977	7.870	18.528	29.086	44.705
beta3_yellow[9]	30.180	8.047	18.442	29.387	44.876
beta3_yellow[10]	30.007	7.911	18.477	29.099	44.978
beta3_yellow[11]	45.285	0.722	43.947	45.415	45.973
beta3_yellow[12]	43.302	0.373	42.554	43.276	44.071
beta3_yellow[13]	44.858	0.407	43.973	44.929	45.526
beta3_yellow[14]	44.159	1.481	42.849	44.269	45.845
beta3_yellow[15]	45.169	0.524	44.162	45.155	45.965
beta3_yellow[16]	44.533	0.826	43.353	44.546	45.843
mu_beta0_yellow[1]	0.106	0.558	-1.082	0.116	1.260
mu_beta0_yellow[2]	0.652	0.325	-0.032	0.668	1.287
mu_beta0_yellow[3]	-2.458	0.654	-3.507	-2.549	-0.866
tau_beta0_yellow[1]	1.790	2.408	0.093	1.127	7.538
tau_beta0_yellow[2]	3.724	4.652	0.336	2.503	14.749
tau_beta0_yellow[3]	1.501	2.634	0.090	0.908	6.062
beta0_black[1]	-0.074	0.160	-0.379	-0.078	0.241
beta0_black[2]	1.917	0.130	1.665	1.918	2.173
beta0_black[3]	1.317	0.136	1.058	1.317	1.586
beta0_black[4]	2.430	0.130	2.177	2.432	2.679
beta0_black[5]	4.630	2.102	1.877	4.196	10.043
beta0_black[6]	4.586	1.924	2.266	4.088	9.853
beta0_black[7]	3.728	1.896	1.515	3.240	8.802
beta0_black[8]	0.958	0.212	0.554	0.953	1.375
beta0_black[9]	2.607	0.226	2.166	2.606	3.043
beta0_black[10]	1.464	0.135	1.201	1.467	1.733
beta0_black[11]	3.485	0.155	3.180	3.488	3.779
beta0_black[12]	4.867	0.175	4.533	4.864	5.203
beta0_black[13]	-0.109	0.251	-0.607	-0.097	0.338
beta0_black[14]	2.852	0.162	2.538	2.856	3.158
beta0_black[15]	1.289	0.154	0.994	1.286	1.600
beta0_black[16]	4.275	0.162	3.952	4.274	4.590
beta2_black[1]	7.771	10.008	0.542	3.449	40.294
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-2.237	1.813	-7.313	-1.662	-0.406
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.743	1.342	39.695	41.952	43.251
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.278	0.775	37.516	39.340	40.591
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.263	0.197	-0.659	-0.264	0.126
beta4_black[2]	0.242	0.190	-0.129	0.236	0.615
beta4_black[3]	-0.935	0.198	-1.322	-0.933	-0.548
beta4_black[4]	0.424	0.215	0.007	0.426	0.841
beta4_black[5]	0.521	1.239	-1.214	0.331	3.480
beta4_black[6]	0.557	1.239	-1.199	0.331	3.830
beta4_black[7]	0.399	1.136	-1.374	0.241	3.183
beta4_black[8]	-0.248	0.314	-0.898	-0.231	0.361
beta4_black[9]	0.837	0.767	-0.258	0.704	2.715
beta4_black[10]	0.050	0.184	-0.317	0.052	0.414
beta4_black[11]	-0.698	0.215	-1.094	-0.696	-0.284
beta4_black[12]	0.164	0.322	-0.435	0.155	0.829
beta4_black[13]	-1.185	0.223	-1.617	-1.185	-0.744
beta4_black[14]	-0.183	0.238	-0.626	-0.190	0.293
beta4_black[15]	-0.882	0.214	-1.316	-0.881	-0.462
beta4_black[16]	-0.596	0.230	-1.052	-0.599	-0.150
mu_beta0_black[1]	1.286	0.911	-0.728	1.326	3.109
mu_beta0_black[2]	2.714	1.048	0.805	2.611	5.141
mu_beta0_black[3]	2.528	0.970	0.451	2.579	4.438
tau_beta0_black[1]	0.613	0.577	0.057	0.435	2.178
tau_beta0_black[2]	0.453	0.588	0.046	0.252	2.063
tau_beta0_black[3]	0.240	0.161	0.050	0.203	0.634
beta0_dsr[11]	-2.882	0.291	-3.431	-2.879	-2.300
beta0_dsr[12]	4.543	0.302	3.997	4.541	5.113
beta0_dsr[13]	-1.348	0.299	-1.960	-1.341	-0.775
beta0_dsr[14]	-3.656	0.502	-4.618	-3.662	-2.666
beta0_dsr[15]	-1.935	0.284	-2.508	-1.929	-1.406
beta0_dsr[16]	-2.988	0.368	-3.716	-2.992	-2.260
beta1_dsr[11]	4.819	0.302	4.223	4.826	5.431
beta1_dsr[12]	7.463	22.307	2.294	5.031	20.475
beta1_dsr[13]	2.862	0.313	2.275	2.850	3.483
beta1_dsr[14]	6.323	0.530	5.292	6.317	7.319
beta1_dsr[15]	3.333	0.292	2.760	3.332	3.918
beta1_dsr[16]	5.806	0.385	5.073	5.798	6.573
beta2_dsr[11]	-8.150	2.383	-13.654	-7.942	-4.296
beta2_dsr[12]	-7.096	2.633	-12.761	-6.939	-2.372
beta2_dsr[13]	-6.455	2.634	-12.088	-6.328	-1.937
beta2_dsr[14]	-6.207	2.650	-11.960	-6.001	-1.902
beta2_dsr[15]	-7.770	2.526	-13.355	-7.464	-3.784
beta2_dsr[16]	-7.880	2.371	-13.413	-7.541	-4.160
beta3_dsr[11]	43.488	0.149	43.211	43.486	43.769
beta3_dsr[12]	33.982	0.836	32.088	34.142	34.815
beta3_dsr[13]	43.248	0.288	42.824	43.193	43.861
beta3_dsr[14]	43.352	0.240	43.077	43.282	43.952
beta3_dsr[15]	43.504	0.189	43.154	43.508	43.851
beta3_dsr[16]	43.437	0.159	43.166	43.423	43.756
beta4_dsr[11]	0.582	0.218	0.163	0.579	1.016
beta4_dsr[12]	0.238	0.442	-0.639	0.236	1.084
beta4_dsr[13]	-0.166	0.223	-0.608	-0.158	0.255
beta4_dsr[14]	0.147	0.255	-0.368	0.149	0.638
beta4_dsr[15]	0.722	0.215	0.306	0.723	1.149
beta4_dsr[16]	0.155	0.230	-0.300	0.154	0.609
beta0_slope[11]	-1.844	0.146	-2.142	-1.846	-1.556
beta0_slope[12]	-4.473	0.266	-5.014	-4.466	-3.981
beta0_slope[13]	-1.338	0.185	-1.738	-1.325	-1.020
beta0_slope[14]	-2.674	0.166	-2.999	-2.679	-2.344
beta0_slope[15]	-1.336	0.149	-1.637	-1.334	-1.047
beta0_slope[16]	-2.741	0.159	-3.051	-2.745	-2.423
beta1_slope[11]	4.486	0.224	4.047	4.488	4.931
beta1_slope[12]	3.992	0.450	3.148	3.990	4.840
beta1_slope[13]	2.727	0.461	2.197	2.646	4.133
beta1_slope[14]	6.322	0.416	5.528	6.309	7.166
beta1_slope[15]	2.999	0.204	2.601	3.001	3.397
beta1_slope[16]	5.288	0.286	4.712	5.285	5.841
beta2_slope[11]	8.685	2.332	5.106	8.347	14.237
beta2_slope[12]	6.612	2.937	1.181	6.659	12.562
beta2_slope[13]	5.336	3.084	0.388	5.222	11.644
beta2_slope[14]	6.374	2.514	2.244	6.210	11.954
beta2_slope[15]	8.177	2.385	4.406	7.846	13.722
beta2_slope[16]	7.817	2.308	4.173	7.518	13.346
beta3_slope[11]	43.461	0.134	43.218	43.458	43.724
beta3_slope[12]	43.348	0.302	42.845	43.317	43.942
beta3_slope[13]	43.459	0.402	42.918	43.398	44.083
beta3_slope[14]	43.266	0.136	43.090	43.233	43.616
beta3_slope[15]	43.485	0.160	43.196	43.482	43.790
beta3_slope[16]	43.372	0.145	43.150	43.352	43.716
beta4_slope[11]	-0.727	0.163	-1.049	-0.725	-0.404
beta4_slope[12]	-1.152	0.462	-2.146	-1.118	-0.344
beta4_slope[13]	0.082	0.164	-0.235	0.080	0.399
beta4_slope[14]	-0.091	0.195	-0.482	-0.089	0.288
beta4_slope[15]	-0.767	0.160	-1.083	-0.767	-0.458
beta4_slope[16]	-0.158	0.175	-0.499	-0.157	0.183
sigma_H[1]	0.200	0.055	0.101	0.196	0.314
sigma_H[2]	0.171	0.031	0.117	0.169	0.238
sigma_H[3]	0.197	0.043	0.118	0.195	0.289
sigma_H[4]	0.419	0.078	0.293	0.411	0.597
sigma_H[5]	0.990	0.209	0.615	0.985	1.428
sigma_H[6]	0.438	0.195	0.066	0.427	0.834
sigma_H[7]	0.311	0.065	0.211	0.303	0.463
sigma_H[8]	0.415	0.089	0.275	0.407	0.605
sigma_H[9]	0.524	0.129	0.331	0.503	0.816
sigma_H[10]	0.212	0.043	0.137	0.209	0.310
sigma_H[11]	0.277	0.046	0.202	0.273	0.380
sigma_H[12]	0.438	0.164	0.210	0.412	0.776
sigma_H[13]	0.214	0.038	0.147	0.210	0.298
sigma_H[14]	0.507	0.091	0.351	0.501	0.703
sigma_H[15]	0.247	0.041	0.176	0.244	0.337
sigma_H[16]	0.224	0.044	0.153	0.219	0.324
lambda_H[1]	3.232	4.295	0.137	1.844	14.281
lambda_H[2]	8.131	7.449	0.800	5.975	26.740
lambda_H[3]	6.397	9.647	0.269	3.226	33.045
lambda_H[4]	0.006	0.004	0.001	0.005	0.018
lambda_H[5]	4.046	9.225	0.038	1.086	28.900
lambda_H[6]	6.550	13.268	0.008	0.892	43.902
lambda_H[7]	0.013	0.009	0.002	0.011	0.035
lambda_H[8]	8.012	9.913	0.135	4.640	35.529
lambda_H[9]	0.015	0.010	0.003	0.013	0.039
lambda_H[10]	0.336	1.246	0.032	0.198	1.151
lambda_H[11]	0.262	0.409	0.011	0.128	1.222
lambda_H[12]	4.809	6.488	0.183	2.728	23.534
lambda_H[13]	3.394	3.059	0.233	2.597	10.941
lambda_H[14]	3.421	4.364	0.247	1.990	14.861
lambda_H[15]	0.029	0.182	0.004	0.017	0.103
lambda_H[16]	0.825	1.157	0.042	0.428	3.901
mu_lambda_H[1]	4.410	1.911	1.266	4.265	8.511
mu_lambda_H[2]	3.873	1.983	0.670	3.648	7.972
mu_lambda_H[3]	3.454	1.821	0.761	3.167	7.455
sigma_lambda_H[1]	8.827	4.310	2.140	8.203	18.407
sigma_lambda_H[2]	8.405	4.714	1.116	7.882	18.473
sigma_lambda_H[3]	6.212	3.984	0.960	5.373	16.279
beta_H[1,1]	6.890	1.116	4.090	7.100	8.510
beta_H[2,1]	9.879	0.483	8.828	9.904	10.761
beta_H[3,1]	8.017	0.778	6.160	8.106	9.312
beta_H[4,1]	9.468	7.663	-6.793	9.705	23.847
beta_H[5,1]	0.141	2.237	-4.624	0.300	3.944
beta_H[6,1]	3.083	4.010	-7.245	4.480	7.835
beta_H[7,1]	0.637	5.611	-11.592	1.084	10.713
beta_H[8,1]	1.322	3.755	-2.468	1.229	3.481
beta_H[9,1]	12.965	5.702	1.004	13.112	23.956
beta_H[10,1]	7.009	1.685	3.603	7.064	10.285
beta_H[11,1]	5.045	3.512	-2.879	5.791	9.844
beta_H[12,1]	2.638	1.050	0.845	2.549	4.877
beta_H[13,1]	9.029	0.908	7.081	9.095	10.504
beta_H[14,1]	2.184	1.001	0.246	2.203	4.114
beta_H[15,1]	-5.940	3.793	-12.800	-6.130	2.237
beta_H[16,1]	3.395	2.601	-0.775	3.061	9.333
beta_H[1,2]	7.908	0.247	7.406	7.911	8.373
beta_H[2,2]	10.027	0.137	9.756	10.029	10.294
beta_H[3,2]	8.953	0.197	8.562	8.954	9.343
beta_H[4,2]	3.545	1.450	0.865	3.512	6.438
beta_H[5,2]	1.955	0.924	0.170	1.961	3.745
beta_H[6,2]	5.714	1.030	3.269	5.887	7.314
beta_H[7,2]	2.630	1.059	0.788	2.562	4.837
beta_H[8,2]	3.002	1.043	1.477	3.127	4.253
beta_H[9,2]	3.537	1.108	1.534	3.501	5.854
beta_H[10,2]	8.204	0.340	7.492	8.210	8.868
beta_H[11,2]	9.764	0.637	8.828	9.641	11.214
beta_H[12,2]	3.954	0.369	3.288	3.934	4.731
beta_H[13,2]	9.122	0.250	8.679	9.111	9.623
beta_H[14,2]	4.013	0.355	3.348	4.018	4.718
beta_H[15,2]	11.331	0.682	9.907	11.364	12.571
beta_H[16,2]	4.528	0.809	2.985	4.515	6.202
beta_H[1,3]	8.454	0.247	8.015	8.435	8.975
beta_H[2,3]	10.065	0.115	9.842	10.063	10.293
beta_H[3,3]	9.614	0.166	9.295	9.612	9.965
beta_H[4,3]	-2.477	0.870	-4.229	-2.460	-0.773
beta_H[5,3]	3.832	0.596	2.614	3.822	4.993
beta_H[6,3]	7.964	1.194	6.366	7.611	10.617
beta_H[7,3]	-2.776	0.640	-4.063	-2.750	-1.556
beta_H[8,3]	5.232	0.480	4.638	5.169	6.099
beta_H[9,3]	-2.876	0.733	-4.345	-2.871	-1.516
beta_H[10,3]	8.674	0.282	8.114	8.675	9.230
beta_H[11,3]	8.541	0.284	7.928	8.565	9.032
beta_H[12,3]	5.250	0.320	4.510	5.286	5.777
beta_H[13,3]	8.846	0.176	8.480	8.849	9.190
beta_H[14,3]	5.723	0.277	5.118	5.747	6.212
beta_H[15,3]	10.380	0.319	9.755	10.382	11.009
beta_H[16,3]	6.264	0.609	4.967	6.324	7.283
beta_H[1,4]	8.259	0.183	7.869	8.274	8.587
beta_H[2,4]	10.128	0.119	9.880	10.136	10.336
beta_H[3,4]	10.120	0.161	9.756	10.134	10.398
beta_H[4,4]	11.789	0.456	10.855	11.801	12.649
beta_H[5,4]	5.488	0.733	4.297	5.398	7.158
beta_H[6,4]	6.986	0.953	4.895	7.273	8.282
beta_H[7,4]	8.275	0.338	7.593	8.278	8.939
beta_H[8,4]	6.713	0.242	6.275	6.727	7.120
beta_H[9,4]	7.219	0.475	6.298	7.220	8.153
beta_H[10,4]	7.732	0.239	7.299	7.726	8.234
beta_H[11,4]	9.385	0.203	8.996	9.385	9.777
beta_H[12,4]	7.139	0.211	6.734	7.134	7.589
beta_H[13,4]	9.044	0.141	8.749	9.045	9.318
beta_H[14,4]	7.733	0.216	7.309	7.731	8.185
beta_H[15,4]	9.461	0.239	8.976	9.466	9.921
beta_H[16,4]	9.350	0.235	8.925	9.342	9.864
beta_H[1,5]	8.982	0.146	8.681	8.986	9.260
beta_H[2,5]	10.785	0.095	10.607	10.782	10.976
beta_H[3,5]	10.918	0.171	10.616	10.910	11.269
beta_H[4,5]	8.397	0.467	7.503	8.390	9.333
beta_H[5,5]	5.438	0.583	3.977	5.479	6.435
beta_H[6,5]	8.869	0.646	7.968	8.708	10.424
beta_H[7,5]	6.753	0.335	6.130	6.750	7.453
beta_H[8,5]	8.215	0.206	7.860	8.203	8.620
beta_H[9,5]	8.195	0.485	7.236	8.203	9.162
beta_H[10,5]	10.090	0.234	9.620	10.088	10.545
beta_H[11,5]	11.513	0.235	11.050	11.515	11.988
beta_H[12,5]	8.484	0.193	8.117	8.481	8.881
beta_H[13,5]	10.012	0.128	9.755	10.014	10.261
beta_H[14,5]	9.196	0.236	8.758	9.184	9.691
beta_H[15,5]	11.168	0.246	10.699	11.163	11.657
beta_H[16,5]	9.925	0.182	9.549	9.928	10.277
beta_H[1,6]	10.179	0.192	9.846	10.165	10.603
beta_H[2,6]	11.511	0.105	11.308	11.511	11.715
beta_H[3,6]	10.816	0.162	10.461	10.827	11.109
beta_H[4,6]	12.867	0.827	11.161	12.898	14.473
beta_H[5,6]	5.881	0.609	4.713	5.875	7.117
beta_H[6,6]	8.816	0.721	6.839	8.963	9.804
beta_H[7,6]	9.865	0.575	8.724	9.864	10.991
beta_H[8,6]	9.525	0.266	9.013	9.542	9.956
beta_H[9,6]	8.475	0.819	6.882	8.460	10.080
beta_H[10,6]	9.507	0.312	8.829	9.534	10.046
beta_H[11,6]	10.818	0.349	10.091	10.838	11.454
beta_H[12,6]	9.374	0.256	8.871	9.370	9.894
beta_H[13,6]	11.052	0.165	10.764	11.038	11.397
beta_H[14,6]	9.827	0.294	9.220	9.833	10.361
beta_H[15,6]	10.834	0.431	9.942	10.846	11.653
beta_H[16,6]	10.542	0.241	10.028	10.551	10.995
beta_H[1,7]	10.878	0.877	8.822	10.987	12.311
beta_H[2,7]	12.213	0.428	11.314	12.219	13.066
beta_H[3,7]	10.553	0.666	9.042	10.623	11.669
beta_H[4,7]	2.585	4.203	-5.452	2.454	11.081
beta_H[5,7]	6.295	1.762	2.973	6.292	9.871
beta_H[6,7]	9.810	2.567	4.767	9.701	16.601
beta_H[7,7]	10.544	2.930	4.776	10.580	16.398
beta_H[8,7]	10.957	0.962	9.498	10.912	12.512
beta_H[9,7]	4.380	4.135	-3.841	4.511	12.394
beta_H[10,7]	9.831	1.447	7.221	9.716	12.966
beta_H[11,7]	10.915	1.760	7.582	10.805	14.839
beta_H[12,7]	10.003	0.971	7.861	10.095	11.611
beta_H[13,7]	11.646	0.754	9.879	11.739	12.793
beta_H[14,7]	10.408	0.953	8.375	10.466	12.030
beta_H[15,7]	12.026	2.224	7.753	11.987	16.503
beta_H[16,7]	12.304	1.300	10.155	12.157	15.361
beta0_H[1]	8.767	14.063	-19.954	9.031	36.046
beta0_H[2]	10.617	6.539	-2.935	10.543	23.466
beta0_H[3]	10.197	10.509	-9.611	9.925	30.900
beta0_H[4]	6.598	184.851	-361.471	7.323	378.123
beta0_H[5]	4.536	21.712	-41.094	4.473	50.306
beta0_H[6]	7.074	52.122	-113.013	7.575	122.749
beta0_H[7]	4.796	135.348	-260.032	3.956	278.664
beta0_H[8]	7.114	35.051	-14.839	6.516	27.388
beta0_H[9]	1.056	125.533	-246.480	0.921	252.156
beta0_H[10]	7.925	33.820	-63.354	8.623	75.784
beta0_H[11]	8.659	51.512	-103.844	9.445	115.414
beta0_H[12]	6.838	12.006	-16.466	6.672	30.585
beta0_H[13]	9.907	11.386	-11.032	9.757	32.067
beta0_H[14]	6.872	11.563	-15.851	7.104	29.217
beta0_H[15]	7.282	103.083	-201.590	6.032	217.250
beta0_H[16]	7.956	25.612	-40.269	7.659	60.801